Another similar idea is the Kempner series. If you add 1/n for all natural numbers n, then the series tends towards infinity. However, if you leave out any in

Another similar idea is the Kempner series. If you add 1/n for all natural numbers n, then the series tends towards infinity. However, if you leave out any integers that contain a digit 9, then the series converges (to just under 23). (It would also converge if you left out numbers containing a digit 3, just to a different limit.)